Bifurcations of a Generalized Heteroclinic Loop in a Planar Piecewise Smooth System with Periodic Perturbations

• Wu, Fang ^[1] ; Huang, Lihong ^[2] ; Wang, Jiafu ^[2]
  1. [1] Hunan University

     Hunan University

     China

     
  2. [2] Changsha University of Science and Technology

     Changsha University of Science and Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022
• Idioma: inglés
• DOI: 10.1007/s12346-021-00554-x
• Enlaces
  • Texto completo
• Resumen

  • This work deals with the periodic orbit bifurcations of a T-periodic perturbed piecewise smooth system whose unperturbed part has a generalized heteroclinic loop connecting a hyperbolic critical point and a quadratic tangential singularity. By constructing several displacement functions that depend on perturbation parameter ε and time t, sufficient conditions of the existence of a homoclinic loop and a sliding generalized heteroclinic loop (that is a generalized heteroclinic loop a part of which lies on the switching manifold) are obtained. As the application, we give a concrete example to show that under suitable perturbations of the generalized heteroclinic loop the corresponding phenomena can appear.

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